Q. If a player scores 10 points for a win and 5 points for a draw in a league, how many points does a player have after 3 wins and 2 draws?
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Solution
The player earns 10 points for each win (3 wins = 30 points) and 5 points for each draw (2 draws = 10 points), totaling 30 + 10 = 40 points.
Correct Answer:
B
— 30
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Q. If a player scores 10 points for a win and 5 points for a draw in a tournament, how many points does a player have after 3 wins and 2 draws?
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Solution
The total points are calculated as (3 wins * 10 points) + (2 draws * 5 points) = 30 points.
Correct Answer:
B
— 30
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Q. If a player scores 10 points for a win and 5 points for a draw in a tournament, how many points does a player have if they won 3 matches and drew 2?
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Solution
Points = (Wins * 10) + (Draws * 5) = (3 * 10) + (2 * 5) = 30.
Correct Answer:
B
— 30
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Q. If a player scores 3 points for a win, 1 point for a draw, and 0 points for a loss, how many points does a player have if they won 5 matches, drew 2, and lost 3?
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Solution
Points = (Wins * 3) + (Draws * 1) + (Losses * 0) = (5 * 3) + (2 * 1) + (3 * 0) = 15 + 2 + 0 = 17 points.
Correct Answer:
A
— 17
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Q. If a player scores 30 points in a game and the average score of the team is 25 points, what can be inferred about the player's performance?
A.
The player performed below average.
B.
The player performed above average.
C.
The player is the worst performer on the team.
D.
The player's score does not affect the team's average.
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Solution
Scoring 30 points indicates that the player performed above the team's average of 25 points.
Correct Answer:
B
— The player performed above average.
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Q. If a player scores 30 points in a game and the winning score is 50 points, what percentage of the winning score did the player achieve?
A.
60%
B.
50%
C.
70%
D.
40%
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Solution
To find the percentage, divide the player's score by the winning score and multiply by 100. (30/50) * 100 = 60%.
Correct Answer:
A
— 60%
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Q. If a polygon has 10 sides, what is the measure of each interior angle in a regular decagon? (2023)
A.
144 degrees
B.
120 degrees
C.
108 degrees
D.
135 degrees
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Solution
The measure of each interior angle in a regular polygon is given by the formula [(n-2) * 180] / n. For a decagon (n=10), it is [(10-2) * 180] / 10 = 144 degrees.
Correct Answer:
A
— 144 degrees
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Q. If a polygon has 10 sides, what is the measure of each interior angle in a regular polygon? (2023)
A.
144 degrees
B.
156 degrees
C.
180 degrees
D.
120 degrees
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Solution
The measure of each interior angle in a regular polygon can be calculated using the formula [(n-2) * 180] / n. For n=10, it is 144 degrees.
Correct Answer:
A
— 144 degrees
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Q. If a polygon has 12 sides, how many diagonals can be drawn from one vertex?
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Solution
The number of diagonals that can be drawn from one vertex of an n-sided polygon is given by (n-3). For a dodecagon (12-sided polygon), it is 12-3 = 9.
Correct Answer:
B
— 10
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Q. If a polygon has 12 sides, what is the measure of each exterior angle in a regular dodecagon?
A.
30 degrees
B.
36 degrees
C.
15 degrees
D.
45 degrees
Show solution
Solution
The measure of each exterior angle of a regular polygon can be calculated using the formula 360/n, where n is the number of sides. For a dodecagon (12 sides), it is 360/12 = 30 degrees.
Correct Answer:
B
— 36 degrees
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Q. If a polygon has 12 sides, what is the measure of each exterior angle in a regular polygon?
A.
30 degrees
B.
36 degrees
C.
60 degrees
D.
90 degrees
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Solution
The measure of each exterior angle of a regular polygon is calculated as 360/n, where n is the number of sides. For a dodecagon (12 sides), it is 360/12 = 30 degrees.
Correct Answer:
B
— 36 degrees
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Q. If a polygon has 8 sides, how many diagonals does it have?
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Solution
Using the formula n(n-3)/2, for an octagon (n=8), the number of diagonals is 8(8-3)/2 = 20.
Correct Answer:
A
— 20
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Q. If a polygon has 8 sides, what is the measure of each interior angle in a regular octagon?
A.
135 degrees
B.
120 degrees
C.
108 degrees
D.
150 degrees
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Solution
The measure of each interior angle of a regular polygon can be calculated using the formula [(n-2) * 180] / n. For an octagon (n=8), it is [(8-2) * 180] / 8 = 135 degrees.
Correct Answer:
C
— 108 degrees
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Q. If a polygon has 8 sides, what is the sum of its interior angles?
A.
720 degrees
B.
1080 degrees
C.
900 degrees
D.
1440 degrees
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Solution
The sum of the interior angles of an octagon (8-sided polygon) is calculated using the formula (n-2) * 180, which gives (8-2) * 180 = 1080 degrees.
Correct Answer:
B
— 1080 degrees
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Q. If a polynomial is expressed as P(x) = 2x^3 - 4x^2 + 3x - 5, what is the coefficient of the x^2 term?
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Solution
In the polynomial P(x), the coefficient of the x^2 term is -4.
Correct Answer:
B
— -4
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Q. If a polynomial is expressed as P(x) = 2x^3 - 4x^2 + 3x - 5, what is the coefficient of x^2?
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Solution
In the polynomial P(x), the coefficient of x^2 is -4.
Correct Answer:
B
— -4
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Q. If a polynomial p(x) is expressed as p(x) = x^2 - 5x + 6, what are its roots?
A.
2 and 3
B.
1 and 6
C.
0 and 6
D.
5 and 1
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Solution
The roots of the polynomial can be found by factoring it as (x - 2)(x - 3) = 0, giving roots 2 and 3.
Correct Answer:
A
— 2 and 3
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Q. If a polynomial p(x) is given by p(x) = x^2 - 5x + 6, what are its roots?
A.
2 and 3
B.
1 and 6
C.
0 and 6
D.
5 and 1
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Solution
The roots of the polynomial can be found by factoring it as (x - 2)(x - 3) = 0, giving roots 2 and 3.
Correct Answer:
A
— 2 and 3
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Q. If a polynomial p(x) is given by p(x) = x^2 - 5x + 6, what are the roots of the polynomial?
A.
2 and 3
B.
1 and 6
C.
0 and 6
D.
5 and 1
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Solution
The roots of the polynomial can be found by factoring it as (x - 2)(x - 3) = 0, giving roots 2 and 3.
Correct Answer:
A
— 2 and 3
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Q. If a polynomial p(x) is given by p(x) = x^3 - 6x^2 + 11x - 6, what can be inferred about its roots?
A.
It has three distinct real roots.
B.
It has one real root and two complex roots.
C.
It has no real roots.
D.
It has two distinct real roots.
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Solution
By applying the Rational Root Theorem and synthetic division, we can find that p(x) has three distinct real roots.
Correct Answer:
A
— It has three distinct real roots.
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Q. If a population of a town increases by 10% every year, what will be the population after 2 years if the current population is 1,000? (2023)
A.
1,100
B.
1,210
C.
1,300
D.
1,400
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Solution
Population after 2 years = 1000 * (1 + 0.10)^2 = 1000 * 1.21 = 1210.
Correct Answer:
B
— 1,210
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Q. If a population of a town increases by 15% every year, what will be the population after 2 years if the current population is 1000? (2023)
A.
1150
B.
1300
C.
1325
D.
1440
Show solution
Solution
After 1 year, the population will be 1000 * 1.15 = 1150. After 2 years, it will be 1150 * 1.15 = 1322.5, rounded to 1325.
Correct Answer:
C
— 1325
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Q. If a population of a town increases by 15% in one year and then decreases by 10% the next year, what is the net percentage change in the population over the two years?
A.
5%
B.
3.5%
C.
4.5%
D.
6%
Show solution
Solution
Let the initial population be 100. After a 15% increase, it becomes 115. After a 10% decrease, it becomes 115 - 11.5 = 103.5. The net change is (103.5 - 100) / 100 * 100% = 3.5%.
Correct Answer:
C
— 4.5%
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Q. If a population of a town increases by 5% every year, what will be the population after 2 years if the current population is 1,000?
A.
1,050
B.
1,102.5
C.
1,100
D.
1,120
Show solution
Solution
Population after 1 year = 1,000 * 1.05 = 1,050. After 2 years = 1,050 * 1.05 = 1,102.5.
Correct Answer:
B
— 1,102.5
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Q. If a product is bought for $150 and sold for $120, what is the percentage loss incurred?
A.
20%
B.
25%
C.
30%
D.
15%
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Solution
Loss = Cost Price - Selling Price = $150 - $120 = $30. Percentage loss = (Loss/Cost Price) * 100 = ($30/$150) * 100 = 20%.
Correct Answer:
B
— 25%
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Q. If a product is marked at $500 and sold at a 30% discount, what is the profit or loss if the cost price is $350?
A.
Profit of $50
B.
Loss of $50
C.
Profit of $100
D.
Loss of $100
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Solution
Selling Price = $500 - (30% of $500) = $500 - $150 = $350. Since Selling Price = Cost Price, there is no profit or loss.
Correct Answer:
A
— Profit of $50
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Q. If a product is marked at $500 and sold for $450, what is the discount percentage offered? (2023)
A.
5%
B.
10%
C.
15%
D.
20%
Show solution
Solution
Discount = Marked Price - Selling Price = 500 - 450 = 50. Discount Percentage = (50/500) * 100 = 10%.
Correct Answer:
C
— 15%
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Q. If a product is sold at a loss of 20% for $80, what was the cost price of the product? (2023)
A.
$100
B.
$90
C.
$80
D.
$70
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Solution
Let the cost price be x. Then, 80 = x - (20% of x) => 80 = x - 0.2x => 80 = 0.8x => x = 100.
Correct Answer:
A
— $100
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Q. If a product is sold for $150 after a discount of 25%, what was its marked price?
A.
$175
B.
$200
C.
$180
D.
$160
Show solution
Solution
Let the marked price be x. After a 25% discount, the selling price is x - (0.25 * x) = 0.75x. Setting this equal to $150 gives 0.75x = $150, so x = $200.
Correct Answer:
B
— $200
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Q. If a product is sold for $150 after a discount of 25%, what was the original price?
A.
$175
B.
$200
C.
$180
D.
$160
Show solution
Solution
Let the original price be x. After a 25% discount, the selling price is x - (0.25 * x) = 0.75x. Thus, 0.75x = $150, so x = $150 / 0.75 = $200.
Correct Answer:
B
— $200
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